TY - JOUR
T1 - Bubbling solutions for a skew-symmetric Chern–Simons system in a torus
AU - Han, Xiaosen
AU - Huang, Hsin-Yuan
AU - Lin, Chang Shou
N1 - Publisher Copyright:
© 2017 Elsevier Inc.
PY - 2017/8/15
Y1 - 2017/8/15
N2 - We establish the existence of bubbling solutions for the following skew-symmetric Chern–Simons system {Δu1+[Formula presented]eu2(1−eu1)=4π∑i=1N1δpi1Δu2+[Formula presented]eu1(1−eu2)=4π∑i=1N2δpi2 over a parallelogram Ω with doubly periodic boundary condition, where ε>0 is a coupling parameter, and δp denotes the Dirac measure concentrated at p. We obtain that if (N1−1)(N2−1)>1, there exists an ε0>0 such that, for any ε∈(0,ε0), the above system admits a solution (u1,ε,u2,ε) satisfying u1,ε and u2,ε blow up simultaneously at the point p⁎, and [Formula presented]euj,ε(1−eui,ε)→4πNiδp⁎,1≤i,j≤2,i≠j as ε→0, where the location of the point p⁎ defined by (1.12) satisfies the condition (1.13).
AB - We establish the existence of bubbling solutions for the following skew-symmetric Chern–Simons system {Δu1+[Formula presented]eu2(1−eu1)=4π∑i=1N1δpi1Δu2+[Formula presented]eu1(1−eu2)=4π∑i=1N2δpi2 over a parallelogram Ω with doubly periodic boundary condition, where ε>0 is a coupling parameter, and δp denotes the Dirac measure concentrated at p. We obtain that if (N1−1)(N2−1)>1, there exists an ε0>0 such that, for any ε∈(0,ε0), the above system admits a solution (u1,ε,u2,ε) satisfying u1,ε and u2,ε blow up simultaneously at the point p⁎, and [Formula presented]euj,ε(1−eui,ε)→4πNiδp⁎,1≤i,j≤2,i≠j as ε→0, where the location of the point p⁎ defined by (1.12) satisfies the condition (1.13).
KW - Bubbling solutions
KW - Non-degeneracy
KW - Skew-symmetric Chern–Simons system
UR - http://www.scopus.com/inward/record.url?scp=85019604180&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2017.04.018
DO - 10.1016/j.jfa.2017.04.018
M3 - Article
AN - SCOPUS:85019604180
SN - 0022-1236
VL - 273
SP - 1354
EP - 1396
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 4
ER -